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arXiv · 2312.03101

Invariant derivations and trace bounds

Skip Garibaldi·Robert M. Guralnick·Eric M. Rains
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Abstract

About 20 years ago, J-P.~Serre announced a bound on the trace of elements of compact Lie groups under the adjoint representation together with related results, provided indications of his proofs, and invited a better proof. This note provides a new, general method for proving such bounds; uses that method to derive Serre's bounds; gives a second proof of Serre's announced results that (we learned) closely follows his original argument; and provides lower bounds for traces of other representations of compact Lie groups and for Brauer characters of finite groups.

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Skip Garibaldi, Robert M. Guralnick, Eric M. Rains. 2023-12-05. Invariant derivations and trace bounds. https://doi.org/10.5802/jep.310

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